Abstract
Gendo-Frobenius algebras are a common generalisation of Frobenius algebras and of gendo-symmetric algebras. A comultiplication is constructed for gendo-Frobenius algebras, which specialises to the known comultiplications on Frobenius and on gendo-symmetric algebras. In addition, Frobenius algebras are shown to be precisely those gendo-Frobenius algebras that have a counit compatible with this comultiplication. Moreover, a new characterisation of gendo-Frobenius algebras is given. This new characterisation is a key for constructing the comultiplication of gendo-Frobenius algebras.
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Acknowledgements
The author would like to thank Steffen Koenig for helpful comments and proof reading. The results in this article are a part of author’s doctoral thesis [9], which was financially supported by DFG.
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Open Access funding enabled and organized by Projekt DEAL. This work was supported by DFG project KO 1281/13-1.
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Presented by: Peter Littelmann
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Yırtıcı, Ç. Gendo-Frobenius Algebras and Comultiplication. Algebr Represent Theor 26, 1849–1864 (2023). https://doi.org/10.1007/s10468-022-10156-z
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DOI: https://doi.org/10.1007/s10468-022-10156-z